NETWORK MODELING OF PERMEABILITY EVOLUTION DURING CEMENTATION AND HOT ISOSTATIC PRESSING

Permeability of rocks may evolve as a complicated function of porosity during hydrothermal compaction. Recent laboratory studies on hot-pressed calcite and naturally lithified Fontainebleau sandstone reveal that there exist three regimes with distinctly different permeability-porosity relationships. At relatively high porosities, permeability changes with porosity reduction following a power law (k(proportional to)phi(alpha)) with an exponent alpha approximate to 3 (regime 1). At low porosities, the power law no longer applies and an accelerated reduction in permeability is found (regime 2). Finally, the permeability becomes too small to be measured, which implies that the pore space is disconnected and there is no percolation (regime 3). Similar behavior and three separate regimes have also been observed in the evolution of electrical conductivity with porosity in hot-pressed quartz. In this study, we developed a unified model based on percolation theory and the simulation of random networks to analyze the evolution of permeability and electrical conductivity in regimes 1 and 2. We incorporated a random shrinkage model and a connectivity loss model in a three-dimensional cubic network to account for the two distinct regimes. In regime 1; we kept the network connectivity at 100% and reduced the diameter of an arbitrary bond by a shrinkage factor randomly distributed between 0 and 1. In regime 2, we reduced the network connectivity from 100% to the percolation threshold while maintaining the same pore size distribution. For Fontainebleau sandstone, the pore size distribution is constrained by microstructural observations from automated image analysis and stereological measurements. For hot-pressed calcite and quartz, since microstructural data were not available, we made preliminary measurements on one available micrograph of a calcite sample. Our simulations predict changes in permeability and pore statistics as a function of porosity which Show good agreement with the laboratory data. In accordance with percolation theory, the ratio between interconnected and total porosities is given by the ratio between the order parameter and the bond occupation probability of the network. Detailed observations of the interconnected porosity and total porosity of calcite during hot isostatic pressing are in good agreement with the theoretical prediction. Implications of our modeling results on the kinetics of healing and diagenetic processes are also discussed.